When we went on our first cruise, we thought it might be better to eat alone. I have to say that I'm so glad that we didn't request it because we made some great friends that we are still in contact with. We always ate breakfast & lunch alone so it was nice having some others to talk to at dinner. We had a great experience on our second cruise as well with our tablemates. We went to Alaska in May and they have the anytime dining thing where you can get a table for just your party or you can sit at a large table with others. We usually just took whatever was available, but sitting alone wasn't that fun.
It's totally up to you if you want your own table, just request it.